What is Singularities: Definition and 178 Discussions

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic p it is an open problem in dimensions at least 4.

View More On Wikipedia.org
Recent contents Top users
  1. MTd2

    How to avoid singularities in AS Gravity? Find non perturbative inflation

    http://arxiv.org/abs/1008.2768 "To pursue our analysis further, we must determine more carefully the relationship between the renormalization scale µ and the density ρ. One appealing choice, advocated by Weinberg in his analysis of inflation in asymptotically safe gravity [3], is to take the...
  2. Z

    Question about gravitatinal singularities and Shwarzchilds Radius.

    Every mass has a Shwarzchild's radius. Once the mass is compressed down to its Shwarzchild's radius, does it necessarily turn into a gravitational singularity, or does it just trap light from leaving? In other words, do all black holes have a gravitational singularity? and do all black holes...
  3. Z

    Question about black holes and graviational singularities.

    Do we know the magnitude of gravitational force needed to violate the Pauli exclusion principle? Also, I my research has told me that violating the principle still isn't enough to turn the fallen star into a black hole. It could still become a neutrons star, so if that is the case, what...
  4. T

    Complex Analysis- Singularities

    Homework Statement Let f be analytic at the complex plane excapt for z= -1 and z=3 which are simple poles of f. Let \Sigma_{-\infty}^{-1} a_{n}(z-2)^{n} be the Laurent series of f. In part A I've found that the series converges at 1<|z-2|<3 . B is: Find the coeefficients a_{n} of the...
  5. P

    Singularities, dark matter, and dark energy. A connection?

    First off, let me say that while I am an avid astronomer, I know very little about the mathematics of astrophysics. My specialty falls more under mechanical engineering. While initially they may not seem all that related, history shows that the mixing of varying disciplines often sparks...
  6. A

    Laurent Expansion Problem (finding singularities)

    Homework Statement Find all Laurent expansion of the function f(z) = 1/(z(8(z^3)-1)) with centre z = 0. The Attempt at a Solution I tried to find all the singularities and came up with z = 0, z = 1/2, z = (1/2)exp((n*pi*i)/3) where n = +-2,+-4,+-6... . But according to the solution n can only...
  7. J

    Singularities in colliding black holes

    When two black holes collide, do their singularities merge the instant their event horizons touch? Or is there a lag between the event horizons touching and the singularities merging when there are actually two singularities inside a single black hole?
  8. D

    Complex Analysis - Essential Singularities and Poles

    Homework Statement Find two analytic functions f and g with common essential singularity at z=0, but the product function f(z)g(z) has a pole of order 5 at z=0. Homework Equations Not an equation per say, but I'm thinking of the desired functions in terms of their respective Laurent...
  9. L

    Geodesic Incompleteness: Exploring Singularities in GR

    Singularities in GR are often associated with geodesic incompleteness. My question is what does it actually mean for a geodesic to be incomplete?
  10. H

    Integral with singularities at the endpoints

    Homework Statement Evaluate the Integral \int dx/((a^2+x^2)*sqrt(1-x^2)) from -1 to 1 Using contour integration Homework Equations Residue theorem/Cauchy integral forumulaThe Attempt at a Solution So I know that at the end-points of the interval (abs(z) = 1) that a singularity exists, so a...
  11. J

    Understanding BH Singularities - Temporal vs Spatial

    Hello I've read that there are two kinds of singularities : temporals and spatial ones. How can we know the kind of a singularity ? What are the differences between spatial and temporal singularities ? Thanks, Jeff
  12. P

    What is the relationship between black holes and singularities?

    OK, this is a long one. Black holes are a singularity, right? As is, their dimensions are 0mX0mX0m? That is why their gravity is so strong, because objects can get much closer and thus make the distance between them 0 and force of gravity infinite. In order for this to be possible, there...
  13. L

    Singularities: Complicated function

    Homework Statement Find all the singularities of f(z) = \frac{{{e^{\frac{1}{{z - 1}}}}}}{{{e^{\frac{1}{z}}} - 1}} in the extended complex field, classify them and find Res(f, 0) and Res(f, infinity) Homework Equations Res(f, z0) = a-1 in the Laurent series around that z0 {e^z} =...
  14. O

    What Are the Singularities in the Extended Complex Plane for (1/s)Ln(s^2+1)?

    Homework Statement (1/s)Ln(s^2+1) Find and classify all singularities in the "extended" complex plane. Draw but do not evaluate the contour you would use to find the inverse laplace transform. Homework Equations (1/s)Ln(s^2+1) The Attempt at a Solution...
  15. C

    Poles or Removable Singularities

    Homework Statement Determine the location and nature of singularities in the finite z plane of the follow function and apply Cauchy Integral Formula Homework Equations g(z) = sin 2z ------- z^15 The Attempt at a Solution I know there is a pole of order 14 at z = o...
  16. D

    Why singularities do not exist

    I posted it in SR/GR but probably it really belongs here: I can explain my motivation. Non red-shifted Hawking radiation is very intense. So when observer approaches the singularity, singularity is always hidden behind the apparent horizon. However, the horizon it covered with a cloud of...
  17. marcus

    Physics does not end at singularities (Abhay at MG12)

    The Marcel Grossmann meeting is a major international conference held every three years--on "recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories." The twelfth in the series--MG12--was in Paris last month. Abhay Ashtekar chaired...
  18. C

    Matter, anti-matter, and singularities

    Lets say anti-matter is less sparse than it currently is. What would happen if two singularities one of matter and one of anti-matter were to merge? Anything special, or the same thing that happens every time matter and anti-matter merge?
  19. I

    Formation of Naked Singularities

    Hi! I've been trying to find explanations about the theoretical formation of naked singularities, and all I could come up with was Wikipedia, and frankly, the explanation didn't "set" in my mind, I couldn't really visualize it. It reads: "From concepts drawn of rotating black holes, it is...
  20. R

    Kerr metric, singularities in Boyer-Lindquist and Cartesian coordinates

    I've found a fairly concise review of the Kerr metric at http://www.physics.mcmaster.ca/phys3a03/The%20Kerr%20Metric.ppt The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley. On slide 6 they give the usual...
  21. N

    Complex Analysis: Poles and Singularities

    Homework Statement Hi all. According to my book, a pole z_0 of a function f(z) is defined as \mathop {\lim }\limits_{z \to z_0 } f(z) = \infty. Now let's look at e.g. f(z) = exp(z). Thus we have a singularity for z = infinity, since the limit in this case is infinity. This is what I don't...
  22. J

    Do any singularities have Infinite density

    Do any singularities (including the big bang singularity) have: 1. Infinite density 2. Infinite mass 3. Volume Also, based on the questions above, are naked singularities different to black hole singularities?
  23. W

    Basic Alg. Geometry: Nodal Singularities. Attn Wonk.

    Hi, everyone : I am reading about "Nodal singularities" ,and I have not been able to find a clear def. of what they are. Neither of the standard sources: Wiki, Google, or some of the books I have checked, has a clear explanation. Here is the context: We are trying...
  24. D

    Naked Ring Singularities and Jets from AGNs

    At first, I don't see any value in the cosmic censorship hypotesis. If ring singularity (RS) is directly observable (interesting how it looks like. Any simulations?) inside the second horizon, why outside we should be afraid to look at that beast? So I started to thing about RS and Jets...
  25. J

    Naked singularities, and Hawking

    I've read that Hawking believes the Universe somehow prevents naked singularities, and made a bet about it with Kip Thorne. But it seems to me that if you take a static black hole and continually inject material into it with high angular momentum, eventually you would have a naked singularity...
  26. S

    Black hole singularities and negative space-time

    I wasn't sure where to put this, so astrophysics seems like a good bet? I'm only fourteen, but I'm incredibly interested in astrophysics, quantum mechanics, black holes and the like. I've read about naked singularities, that they can occur the black hole's charge is great enough and the...
  27. N

    What is the exact physical extent of a black hole singularity?

    If a large (>1.5 SM) conventional star collapses to become a black hole, textbooks say that a singularity will form in the BH. A singularity is characterized by a gravitational field of infinite potential. (Or infinite spacetime curvature if you prefer that terminology). 1. As I understand...
  28. diegzumillo

    Normalization and singularities

    Hi There! Being direct to the point: Does normalization removes singularities? Such as infinite. I came up with this question because, while I was working with a not normalized function, I reached a very strange result. There are two points where the probability tends to infininte...
  29. D

    Integrating through singularities

    I am a little bit confused about dealing with integrals around singularities because my professor seems to treat some situations more rigorously than others. We talked this integral and said \int_{-\infty}^{\infty}\frac{1}{x^3} dx = undefined This seems a little bit unintuitive to me...
  30. D

    Are Singularities One-Sided in Terms of Time?

    Singularities are places where time ends for anything in them. In other words, if Bob falls into a black hole at 2:00, time will end for the matter in his body and he won't exist time-wise past 2:00. But according to the Big Bang theory, the universe began in the form of a singularity. Obviously...
  31. N

    Poles, zeroes, and essential singularities of z^(2/3)

    Homework Statement Identify the zeroes, poles and essential singularities of f(z) = z^{2/3} Homework Equations f(z) = e^{\frac{2}{3}\log{z}} Which I'm not sure will be useful... The Attempt at a Solution I know that f is 0 at z=0, but what is the order of this zero? Is there such a...
  32. K

    Differential equations with singularities

    I have to solve the following coupled differential equations d^2f(r)/dr^2+1/r*df(r)/dr+(2-2*f(r)^2-2*a*g(r)^2-l_1^2/r^2)*f(r)=0 d^2g(r)/dr^2+1/r*dg(r)/dr+(2-2*g(r)^2-2*a*f(r)^2-l_2^2/r^2)*g(r)=0, where a is the coupling. I think that it is not possible to solve it analytically (even in...
  33. michael879

    Naked Singularities: Questions on Fund. Particles as Black Holes

    I have a few questions about these. My main question concerns the "theory" that all fundamental particles are actually black holes. If this were the case, at least for an electron, they would be naked singularities because q+a > m. 1) What are the effects of a naked singularity that make...
  34. marcus

    At the April APS meeting: curing cosmic singularities

    One of the sessions at the April meeting of the American Physical Society (APS) will be on what replaces classic GR singularities (like bigbang or black hole) when you move to a quantized theory. Abhay Ashtekar will discuss this from the Loop side. Gary Horowitz will discuss the String side of...
  35. R

    Understanding Spinning Black Holes: A Confused Perspective

    Okay, I know there is observational evidence for spinning black holes, so therefore I must be confused about something, and I want you to tell me what. If you have a star that is spinning, therefore it has orbital angular momentum (mass revolving around a point), then as it is collapsing in...
  36. C

    Exploring the Possibility of Singularities in the Universe

    Hi I'm not very clued up on the mathematics behind these things and I tried searching for relevant threads but everything I found was a bit over my head so sorry if this has come up loads of times before but I was hoping someone might be able to explain in simple terms the reasoning behind...
  37. N

    Singularities and conservative vector fields

    I have a question regarding conservative vectorfields and singularities. Suppose we have a vectorfield who is defined everywhere in R^2 except at the origin where it has a singularity, and suppose it's curl is zero. We then have that it is conservative in every open, simply connected subset in...
  38. F

    Is there an elegant way to find the singularities of an algebraic variety

    Let V be the variety of the ideal (f) a singular point is a point where all the partial derivatives of the f are zero. I know you can find singular points by writing down all these partial derivatives and also that the points are zeros of f (such as all points on the variety) and solve that...
  39. Simfish

    How do singularities of a function on a complex plane affect real line behavior?

    consider the function \frac{1}{\epsilon^2 + z^2} So we know that there are two poles, one at z = i \epsilon, one at z = - i \epsilon. So when this function never hits 0 on the real line, how do the singularities affect its behavior on the line? Okay, so poles are a subclass of singularities...
  40. K

    Poincaré conjecture - singularities - quantum cohomology

    In 2006, the mathematically rigorous proof of the Poincaré conjecture was completely excepted. The Poincaré conjecture was put forward by Henri Poincaré in the early 1900's. It is a theorem about the characterization of the 3D sphere amongst 3D manifolds. It was considered one of the most...
  41. B

    Integral where I need to classify the singularities

    Hi I'm just working on an integral where I need to classify the singularities of the integrand \frac{{\sin \left( {\pi z} \right)}}{{z^4 - 1}}. There are singularities at z = \pm 1, \pm i but the ones I'm interested in are at z = \pm 1. \frac{{\sin \left( {\pi z} \right)}}{{z^4 -...
  42. M

    Understanding Singularities in Complex Functions

    Homework Statement Determine if the following are removable, pole (with order), or essential singularities. a) f(z) = (z^3+3z-2i)/(z^2+1) a=i b) f(z) = z/(e^z - 1) a=0 c) e^e^(-1/z) a=0 2. The attempt at a solution Part a is pretty straightforward, just simplify it down to...
  43. H

    Naked Singularities and the predictibilty problem

    Homework Statement i have a problem about the naked singularities which are appeared in einstine' s solution and mathematically possible ... in that i have readed that for the weak conjecture states (by the penrose and hawking singularity theorems ) that all singularities in gravitational...
  44. marcus

    Singularities and Quantum Gravity

    This just out: http://arxiv.org/abs/gr-qc/0702144 Singularities and Quantum Gravity Martin Bojowald 41 pages, lecture course at the XIIth Brazilian School on Cosmology and Gravitation, September 2006 IGPG-07/2-4, NSF-KITP-07-19 "Although there is general agreement that a removal of...
  45. Loren Booda

    Have absolute gravitational singularities ever formed?

    What of the possibility that dark energy prevents total gravitational collapse of black holes, and might also have helped avoid an actual singularity at the big bang?
  46. J

    Was lqg assessed unfairly at KITP program in quantum nature of singularities?

    Specifically what I`m referring to is the final discussion summing up the program in which the weakness of lqg was characterized explicitly as "the whole theory". Was this a constructive way to end the program? Perhaps some of you would rather ignore this.
  47. M

    Smooth deformation of a Lorentzian manifold and singularities

    How can a smooth deformation of a Lorentzian manifold possibly create one or more singularities?
  48. L

    Singularities and Kasner solution

    Homework Statement Investigate the possible behaviour of the singularity as t \rightarrow 0 in the Kasner solution. Homework Equations The metric for the Kasner solution is given by ds^2 = c^2dt^2 - X_1^2(t)dx_1^2 - X_2^2(t)dx_2^2 - X_3^2(t)dx_3^2 The Attempt at a Solution I...
  49. marcus

    GReat talk by Ashtekar at the kitp singularities workshop

    http://online.kitp.ucsb.edu/online/singular_m07/ go here for Ashtekar talk http://online.kitp.ucsb.edu/online/singular_m07/ashtekar/ I found it works best when I click on "download the whole movie", which takes 5 minutes or so and then I have it on desktop so i can listen to it again. the...
  50. J

    Joris van Hoboken's thesis on Platonic solids,Kleinian singularities and ADE

    In "week182", back in 2002, I referred to this very nice thesis: Joris van Hoboken, Platonic solids, binary polyhedral groups, Kleinian singularities and Lie algebras of type A,D,E, Master's Thesis, University of Amsterdam, 2002, available at...
Back
Top